12 Design of Experiments

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Location Effect?
Operating Windows
Defined:
ቤተ መጻሕፍቲ ባይዱ
Output Variable
Input Variable
4
TQM - University of Michigan
2
Design of Experiments
Pat Hammett
Summary of Terminology
13
Using Excel to Solve the DOE
Must code variables for regression: diameter (-1 = small ; 1= large) length (-1 = medium ; 1 = tall) particle size (-1 = small ; 1 = large) Code: -1 or 1
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If an input variable does not affect the output, then a mfg may either:
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Ignore the variable. Establish control plan to insure that input continues to have no impact on output.
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Identify robust levels and establish controls to maintain, Fix the settings for an input variable, or Remove input variable effect by re-designing process.
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Suppose you wish to study three variables (factors) with two levels for each variable.
Experimental Combinations = LF = 23 = 8 combinations (Full Factorial Design) L = # of Levels, F= # of Factors
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Input Variables
Model (FIRM)
10
TQM - University of Michigan
5
Design of Experiments
Pat Hammett
Example 2: Detergent Box Filling Experiment
Experiment: Determine the effect of three process input variables or factors on the fill rate of a box-filling machine for detergent powder. (goal or target = fill rate = 3.0 kg/s) Process Output Variable or Response: Fill Rate Process Inputs (Factors):Settings of Process Parameters (Levels) Diameter of Chute Short - 4" Long - 6" Length of Chute Detergent Particle Size Medium - 8" Small Tall - 12" Large
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FIRM Approach to DOE Variables
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For each potential input variable identified, determine a model strategy.
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F - fix the settings for input variable I - ignore the settings for an input variables R - randomize the settings for an input variable M - model the variable - identify settings for your variables in which you want to test.
4
Design of Experiments
Pat Hammett
Experimental Combinations
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The number of experimental combinations is based on the:
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number of factors (input variables), number of levels for each factor, number of factor interactions you wish to study.
Output Variable
Input Variable
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Experimental Design and DFSS
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In Design for Six Sigma (DFSS), use DOE to:
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Identify key input variables which affect the mean or variation of a key product output variable. After determining key inputs, mfgs should either:
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TQM - University of Michigan
3
Design of Experiments
Pat Hammett
Conducting an Experiment
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Identify the process output(s) of concern. Identify process input variables which you believe affect the process output. Select input variables to study.
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How many total combinations would you have if you tested 2 factors at 2 levels and 1 factor at 3 levels?
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Example 1: Catapult Experiment (In-class)
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Process Output Variable
Uncontrollable Variables - environmental factors those that are difficult or very expensive to control. (e.g., ambient temperature)
2
TQM - University of Michigan
1
Design of Experiments
Pat Hammett
Duality of Signal & Noise Factors
Effect of Input Variables on a Process Output Adjustment Factors affects the mean of the process without affecting variation "knob". Need these to center a process. (especially if Pp is high, Ppk low) Example: tool position knob in machining
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Most input variables have a robust operating window in which the output is insensitive or able to meet manufacturing specifications. (i.e., relatively few pure linear relationships).
Process Inputs (Factors): Diameter of Chute Average Fill Rates Small: 1.23 Large: 3.20 (1.0+1.3+1.2+1.4)/4 (2.8+3.2+3.5+3.3)/4 Medium: 2.10 Tall: 2.35 (1.0+1.3+2.8+3.2)/4 (1.2+3.5+1.4+3.3)/4
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Remember the cost of experimentation can grow significantly if too many variables and/or levels of variables are selected.
8
TQM - University of Michigan
Are these input variables controllable or uncontrollable?
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Input Variable Combinations
(full factorial model)
Diameter Length Size
Small Medium Large Small Large Small Long Medium Large Small Tall Large
Length of Chute
Detergent Particle Size
Small: 2.12 Large: 2.30 (1.0+2.8+1.2+3.5)/4 (1.3+3.2+1.4+3.3)/4